The 16-year-old was abducted from her home when her family was away to attend a wedding and raped by the men in a forested area of Jharkhand state on Thursday, a local police officer said.
The family complained to the local village council which on Friday ordered the accused to do 100 sit-ups and pay a fine of 50,000 rupees.
Village councils of local elders often settle disputes, bypassing India's lengthy and expensive judicial system. Although they carry no legal weight, they exert massive influence over rural life.
Police said the punishment enraged the men, who beat the girl's parents before setting her on fire.
Two teenagers gang raped in India, one commits suicide
"The two accused thrashed the parents and rushed to the house where they set the girl ablaze with the help of their accomplices," Ashok Ram, the officer in charge of the local police station, told AFP.
"The accused men are absconding. A special investigation team has been set up which is looking into the case."
The incident comes as India reels under a string of violent sexual crimes despite tightening of laws.
Indian woman 'lets' boyfriend rape 13-year-old niece
On Friday, a 55-year-old man allegedly committed suicide after being accused of raping a nine-year-old in southern Andhra Pradesh state, the Press Trust of India reported.
Protests have been held across the country since horrific details emerged last month about an eight year-old girl being gang-raped and murdered in Jammu and Kashmir.
Child rape case heightens India's Hindu-Muslim divide
Some 40,000 rape cases were reported in 2016, with many more believed to go unreported because of stigma attached to sex crimes in deeply patriarchal India.
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